The present and future generations of satellites need to operate with small earth terminals as with mobile vehicle or hand held terminals. Such satellites need to be user oriented in that the user terminal needs to be relatively less complex and have small power, weight and low cost requirements. Such communications systems may be realized at the cost of increasing the complexity of the space borne equipment and central earth stations. An example of such a communication system includes an uplink that uses frequency division multiple access (FDMA) signaling with low cost and complexity terminals while the downlink uses time division multiple access (TDMA) signaling to maximize the satellite radiated power without intermodulation noise. In such communication systems, the small earth terminals do not need the capability of transmitting at very high burst rate and stringent satellite frame synchronization capabilities necessary for TDMA transmitter. The feasibility of mixed mode multiple accessing techniques require efficient means of translation between the two formats of multiple access signaling. Although analog designs can be readily realized, implementation considerations as to size, weight, cost, flexibility, and direct digital processing are expected to achieve higher performance. Digital processing can also fully exploit advances in VLSI and ASIC technologies to achieve improved performance. In wideband satellite systems, various digital signal processing methods are required by the satellite payload. Various methods of conventional digital signal processing include polyphase filtering, Fast Fourier Transform (FFT) filtering, Discrete Fourier Transform (DFT) filtering, frequency domain filtering, multistage bank filtering, and tree filter bank filtering methods. Prior digital signaling processing methods are available for translation and channelization using analytical digital signal processing methods.
In broadband satellites having nominal bandwidths in GHz regimes, major limitations are inherent in analog to digital (AD) conversion of the received broadband signal. Such A/D conversion needs to operate at least at a rate equal to two times the received signal bandwidth. This high-speed conversion rate imposes limitations on the ability of A/D converters operating at such high speeds as well as increasing power requirements and costs. In such situation, an analog filter bank may be required to first split the signal into several signals of smaller bandwidth and then digitally process each individual split signal. Such a hybrid analog and digital structure suffers from the disadvantages of the analog processing in terms of weight and power requirements of the analog filters and lacks the advantages of completely digital processing.
Present day technology involves such processing on board the satellite. An example of such a communication system uses messaging service signals communicated through satellites. In such a communication system, a forward link takes messages from an earth station to the satellite that retransmits to mobile devices through spot beams. The return link begins at the mobile devices up to the satellite and then terminates at an earth station. In such a communication system, the types of transmitter and receivers in the forward and reverse links are different. Thus, optimum uplink and downlink designs to and from the mobile devices and the earth station are different.
In one proposed communication system, the uplink uses FDMA signaling with low cost and low complexity terminals while the downlink uses TDMA signaling to maximize the satellite radiated power without intermodulation noise. In such a communication system, the small earth terminals do not need the capability of transmitting at very high burst rates nor with stringent satellite frame synchronization capabilities necessary for the TDMA transmitters. In another proposed communication system, the uplink is based on random access processing while the downlink uses TDMA. In terms of modulation, all such communication systems make use of digital techniques with inherent advantages in terms of power efficiency, flexibility, error correction and detection, coding, and encryption. The feasibility of mixed mode multiple accessing signaling methods require efficient means of signaling translation between the two formats of multiple access signaling. Such a signaling translation may involve conversion of an FDMA signal into a TDMA multiplexed signal that is then processed through a digital switch to various TDMA carriers being transmitted over the spot beams. Such signaling translations are also useful for switching FDMA carriers to different spot beams without requiring arrays of analog bandpass filters and converters. The FDMA to TDMA signaling translations involve digital channelization and switching of multiplexed channels. Digital channelization uses a digital channelizer that employs conventional digital processing methods. A digital channelizer separates and downconverts incoming multiple signals such as FDMA signals into multiple baseband signals for digital processing or for transmission over a downlink in another signaling format such as TDMA.
The analytical signal processing method is a conventional digital channelization processing method that processes multiplexed channels and utilizes analytical signal properties to reduce the channelizer complexity. The analytical signal processing method allows for relaxed filter specifications of the digital channelizer for reducing implementation complexity. In analytical signal processing systems, the high rate sampled FDMA signal S(f) with NC number of multiplexed channels, after analog down conversion of the received signal to IF range, is first filtered by an analytic complex band pass filter {overscore (H)}i(fTu) where {overscore (H)}i(fTu) is a frequency translated version of a prototype low pass filter {overscore (H)}(fTu) defined by a {overscore (H)}i(fTu) equation.{overscore (H)}l(fTu)={overscore (H)}[(f−(i+½)w)Tu]; i=0, 1, . . . (Nc−1
In the {overscore (H)}i(fTu) equation, Tu is the input signal sampling period and w denotes the bandwidth of any one of the multiplexed channels with equal bandwidth. The filter output is decimated by Nc in the decimator following the filter. The output of the decimator is filtered by a complex low pass analytical filter with a frequency response {overscore (G)}i(fTd) to yield the channelized signal in analytical form. The analytical filter is {overscore (G)}i(fd′) where fd′=fTd and has the frequency response defined by an {overscore (G)}i(fd′) equation.
                    G        _            i        ⁡          (              f        d        ′            )        =      {                                        1            ;                                                0            <                          f              d              ′                        <            0.5                                                            0            ;                                                              -              0.5                        <                          f              d              ′                        <            0                              
From the Nyquist sampling theorem, the decimator output spectrum Y is related to the input X by an Yi(f′d) equation.
                    Y        i            ⁢              (                  f          d          ′                )              =                  1                  N          c                    ⁢                        ∑                      j            =            0                                              N              c                        -            1                          ⁢                              X            i                    ⁢                      (                                          f                d                ′                            -              j                        )                                ;            f      d      ′        =          f      ⁢                          ⁢              T        d              ;            T      d        =                  N        c            ⁢              T        u            
To eliminate any aliasing due to j≠0 terms in the Yi(f′d) equation, the transition band for filter {overscore (H)}i(fTu) should be limited to a bandwidth w on either side of the passband because the images of the spectrum Xi(fd′) are separated by fd′=1 or in terms of frequency f by 2w Hz and thus the transition band effects only the spectrum intervening the images of the desired spectrum, which is filtered by {overscore (G)}i(fd′).
Thus, the channel signal can be recovered with no aliasing error even though filter {overscore (H)}i(fTu) has a transition band of w Hz on either side. The transition band however, makes the design of the filter easier. The output Ū(fTd) is in analytic form. To obtain the corresponding real valued signal, one obtains the complex-conjugate part of the spectrum Ū(fTd). Representing analytic functions {overscore (H)}i and {overscore (G)}i as a sum of the respective conjugate symmetric parts Hi and Gi and anti symmetric parts Hi′ Gi′, the equivalent implementation of the analytic signal approach can be derived. In this equivalent implementation, the signal S(fTu) is first filtered by two filter branches. The first branch consists of a cascade of Hi(fTu), a decimator by Nc and filter Gi(fTu). The second branch consists of a cascade of Hi′(fTu), decimator by Nc, and filter Gi′(fTu). The outputs of the two branches is summed and multiplied by (−1)in to yield the desired channelized signal. The operation of multiplying by (−1)in where n denotes discrete time index and i is the channel number in time domain corresponds to frequency shift of w and is required for odd channels. For even channels (i even) (−1)in≡1 and no additional operation is involved.
In terms of computational complexity, the number of multiplications MAS required per input channel per second is given by the following MAS and K equations.
            M              A        ⁢                                  ⁢        S              =          κ      ⁢                          ⁢              w        2            ⁢                                    w            ⁢                          (                                                N                  C                                +                4                            )                                -                      2            ⁢                          B              ⁢                              (                                                      N                    C                                    +                  2                                )                                                                          (                          w              -              B                        )                    ⁢                      (                          w              -                              2                ⁢                B                                      )                                    κ    =                  -                  2          3                    ⁢              log        ⁡                  [                      5            ⁢                          δ              1                        ⁢                          δ              2                                ]                    
In the K equation, δ1 and δ2 denote the specified in-band and out-of-band ripple respectively, and B denotes the filtering bandwidth of the channelizer. The filtering bandwidth in general is smaller than w to allow for guard bands.
In a direct implementation of the polyphase digital Fourier transform (PDFT) approach for an analyzer synthesizer model, the input signal x(n) is demodulated by the exponential function e−jωkn, low pass filtered by the filter h(n) providing a resulting signal that is down sampled by a factor M. The synthesizer model interpolates all the channel signals back to the high sampling rate, filters the signal by filter f(n) to remove the imaging components, and modulates the resulting signal by complex exponential function ejωkn to translate the resulting signal back to frequency ωk. The output of the synthesizer is the sum of the K channel output signals.
            x      ^        ⁢          (      n      )        =            ∑              k        =        0                    K        -        1              ⁢                            x          ^                k            ⁢              (        n        )            
The polyphase realization of the DFT filter bank is based on the polyphase implementation of the decimators and interpolators. Such a realization is relatively simple for the case of critically sampled filter banks wherein M=K. In this case the number of independent channels Nc is also equal to K. Designs for other choices of M and K are relatively more complex. In the case of M=K, the center frequencies of the K frequency bands are given by an ωk equation.
                    ω        k            =                        2          ⁢          π          ⁢                                          ⁢          k                K              ;          k      =      0        ,  1  ,  …  ⁢          ,            K      -      1        ;          K      =      M      
The analyzer synthesizer model can be shown to be equivalent to the integer band model where, in the analyzer, the input signal x(n) is filtered by a bandpass filter of impulse response hk(n), the output of which is decimated by M to provide xk(m). In the synthesizer, the input channel signal {circumflex over (x)}k(m) is first interpolated by M and the resulting signal is bandpass filtered with filter of impulse response fk(n) to provide xk(m). Sum of all the xk(m), k=1,2, . . . ,K then provides the synthesizer output.
The filter impulse response functions hk(n) are given by hk(n) equations.hk(n)=h(n)WKkn; WK=ej2π/K=WM; fk(n)=f(n)WKkn
An Xk(m) equation follows from the hk(n) equations.
            X      k        ⁢          (      m      )        =            ∑              n        =                  -          ∞                    ∞        ⁢                  h        ⁢                  (          n          )                    ⁢              W        M                  k          ⁢                                          ⁢          n                    ⁢              x        ⁢                  (                                    m              ⁢                                                          ⁢              M                        -            n                    )                    
With change of variables n=rM−i, the xk(m) equation can be rewritten as alternative Xk(m) equations.
            X      k        ⁢          (      m      )        =                    ∑                  i          =          0                          M          -          1                    ⁢                        ∑                      r            =                          -              ∞                                            r            =            ∞                          ⁢                                                            p                _                            i                        ⁢                          (              r              )                                ⁢                      W            M                                          -                k                            ⁢                                                          ⁢              i                                ⁢                                    x              i                        ⁢                          (                              m                -                r                            )                                            =                  ∑                  i          =          0                          M          -          1                    ⁢                        W          M                                    -              k                        ⁢                                                  ⁢            i                          ⁡                  [                                                                      p                  _                                i                            ⁢                              (                m                )                                      ⊗                                          x                i                            ⁢                              (                m                )                                              ]                    
In the Xk(m) equation, {circle around (X)} denotes convolution, and {overscore (p)}i(m) is the impulse response of the ith polyphase branch given in terms of h(n) as {overscore (p)}i(m)=h(mM−i) for i=0, 1, through M−1, and branch input signals xi(m) are given as xi(m)=x(mM+i).
The alternative Xk(m) equations lead to the polyphase DFT filter bank structure. This structure comprises a commutator that demultiplexes the input signal into K=M signals xi(m), each of which is filtered by its corresponding polyphase filter {overscore (p)}i(m). The outputs of the K filters are processed by a K point FFT processor whose outputs comprise the samples of the K channel signals.
Similarly the polyphase DFT filter bank synthesis structure is derived whose polyphase filters have impulse response given by a qi(m) equation.qi(m)=f(mM+i); i=0,1, . . . , M−1
The polyphase implementation has the advantage of reducing the computational requirements by order K compared to direct form. In terms of polyphase branch filter design there are two broad categories of design, including finite impulse response (FIR) and infinite impulse response (IIR) filters. The FIR filters can be designed on the basis of windows using Hamming, Hanning, or Kaiser techniques, optimal equiripple linear phase design based on Chebyshev approximation and a multi-exchange Remez algorithm, half band filters that further reduce the computational requirements, and filter designs based on direct optimization of a criterion function. The IIR filter can be designed as in the classical approach or may be based on a transformation wherein the denominator is a polynomial in ZM and thereby exploits the interpolator and decimator structure to minimize the computational requirements.
The polyphase implementation effectively allows sharing one lowpass filter among all the channels with the help of FFT transform. The total number of real multiplications required per second per channel is found by an MPDFT equation.
      M          P      ⁢                          ⁢      D      ⁢                          ⁢      F      ⁢                          ⁢      T        =      2    ⁢          w      ⁡              [                                            [                                                2                  3                                ⁢                                  log                  ⁡                                      [                                          1                      /                                              (                                                  10                          ⁢                                                      δ                            1                                                    ⁢                                                      δ                            2                                                                          )                                                              ]                                                              ]                                      (                              w                -                                  2                  ⁢                  B                                            )                                +                      4            ⁢                                          log                2                            ⁢                              (                                  N                  C                                )                                                    ]            
The frequency domain filtering (FDF) method is based on the use of FFT techniques in the filtering operation. In time domain, the filtering operation consists of discrete convolution of the sampled input signal with the filter impulse response. Equivalently the result can be obtained by multiplying the Fourier transform of the input signal with filter frequency response and taking the inverse transform of the result. This is the basis of FDF techniques. Even though this approach may seem to be more indirect compared to direct convolution used in FIR filter implementation, this can be made computationally more efficient by using FFT technique in computing the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). However, the application of FFT results in a circular convolution of the input signal segment and the filter impulse response instead of the desired linear convolution. This problem is overcome by an appropriate modification of the straightforward FFT approach. Two such modification techniques, the overlap-save sectioning and the overlap-add sectioning, are well known. Modification techniques use Q to denote the filter impulse response length and N be the sequence length selected for the FFT operation, where N is greater than Q. The term N can of course be selected in an optimal manner so as to minimize the overall computational complexity.
In the overlap-save section method, the incoming signal is segmented into sections of length N such that the adjacent sections have an overlap of (Q−1) samples. Each such section is circularly convolved with the filter response also of length N after padding with zeros, using FFT approach. The first (Q−1) samples of the result are discarded for each section and the truncated sections are concatenated to yield the desired linear convolution. In the overlap-add sectioning method, the input signal is segmented into disjoint sections of length N–Q. Each section is augmented by a sequence of zeros of length Q to yield a sequence of length N, which is circularly convolved with the augmented filter impulse response using FFT techniques. The resulting sequences are aligned in such a manner that there is an overlap of length Q between the successive sequences. During the period of no overlap, individual sequences then provide the desired response. During the periods of overlap, the two overlapping sequences are added to yield the desired output. Both the overlap-save sectioning and overlap-add sectioning methods provide the desired linear convolution.
A specific channelization scheme is known as an FDF channelization scheme that uses an overlap-save approach. An example of a specific channelization scheme uses a 50% overlap, that is, N=2Q. The FDF channelization scheme considers an FDMA signal of 6.0 MHz bandwidth consisting of 300 channels of 20.0 KHz bandwidth each. Simulations in the frequency domain indicate that each channel must have at least sixteen samples points corresponding to a resolution of 1.25 KHz. Thus, for the complete band, at least 4800 points are required. Rounding up to the nearest power of two, an FFT size of 8192 was selected. In terms of Nc, the length for FFT operation is N≅16NC. The number of multiplications for an FFT or IFFT of size is given by Nlog2N. For the implementation requiring only one IFFT, the number of multiplications is equal to 2N[log2N+4]. For real time operation, the operations must be performed in (NTs/2) sec, where Ts is the sampling period of the FDMA signal and the factor 2 accounts for 50% overlap. Therefore the number of multiplications per second is given by an MDFF equation.MDFF=4fs log2[16Nc+4]
In the MDFF equation, fs=1/Ts is the sampling rate selected equal to 10.24 MHz. In practice the number of IFFTs will be determined by the number of outputs of the digital transplexer that may be connected to different spot beams in the satellite communication applications. For example, when there are twelve beams analyzed, the number of operations given by the MDFF equation is roughly multiplied by the number of the outputs.
The multistage (MS) approach provides a means of channelization using successive stages of half-bank filters. Therefore, this technique is appropriate only when NC=2L where L denotes the number of stages of filtering and decimating. This method provides moderate flexibility and computational efficiency, but the efficiency decreases as the number of channels decreases. The total number of real multiplications required per second per channel is found to be in an MMS equation.
      M          M      ⁢                          ⁢      S        =            [                                    (                                                                                N                    F                                    +                  1                                2                            +              1                        )                    ⁢                      (                                                            log                  2                                ⁢                                  N                  C                                            -                              1                2                                      )                          +                  N          G                    ]        ⁢    2    ⁢    w  
In the MMS equation, NF denotes the number of coefficients of the half band filters, NG is the number of coefficients of the last filter of the tree, and w and NC are defined previously.
The communication of broadband signals require A/D converters operating at a very high rate imposing limitations in terms of availability and power requirements. The A/D conversion is a major limitation in extending DSP applications to higher and higher bandwidth signals. A flash type of A/D conversion may be required for conventional implementation. In a given state of A/D conversion technology, there are severe restrictions in terms of availability, the cost and power requirements versus the required sampling rate, and A/D conversion accuracy measured in terms of the number of bits per sample. Thus for a wide band signal, in conventional implementation, the A/D converter may not be available, may not have the required number of bits, or may require excessive power, or may be exceedingly expensive.
In wideband systems, the channelization may be performed in a number of hierarchical stages and in principle different stages may apply different channelization techniques including both digital and analog as hybrid techniques to obtain the most flexible and optimum overall architecture. For example, when the total band is 500.0 MHz, the band may be divided first into six channels each with an 80.0 MHz bandwidth. This stage may be implemented using surface wave acoustic SAW filters or one of the digital techniques. The second stage channelizer may divide the 80.0 MHz band in to four bands of 20.0 MHz band each. This stage may be implemented by the polyphase FFT approach or the analytical approach. The third stage is used to separate signals with bandwidth ranging from 64.0 KHz to 10.0 MHz. A frequency domain filtering approach using pipeline FFT architecture or a multistage tree approach may be used for this stage. There are many possible variations for such a multistage hybrid channelizer.
Digital TV receivers with polyphase analog-to-digital conversion of baseband symbol coding is taught by Limberg in U.S. Pat. No. 5,852,477. Limberg teaches the use of multiple, that is parallel, analog-to-digital converters (ADC) for filtering a single baseband channel in the digital TV receiver. The signal comprises several time-interleaved data streams. In the present disclosure, use of parallel ADCs is taught for the purpose of separating many (N) channels with different carrier frequencies in a FDM format. In most direct digital implementation, the composite signal is first sampled at a high rate of at least two times the bandwidth of composite signals followed by a bank of bandpass filters centered around the incoming channel carrier frequencies. This procedure is referred to as channelization. Limberg does not teach a channelizer procedure. The signal at the input to the bank of ADCs is a real baseband signal. In the channelizer application, the signal is either a complex baseband signal or a complex IF signal obtained by a complex mixer, the latter is preferably used in this application instead of an alternative Hilbert transform approach for implementation simplicity for achieving a complex IF analytic signal. An analytic signal is one where the spectrum of the analytic signal is zero for negative frequencies. Limberg does not teach such frequency separation and downconversion. Limberg teaches the use of multiple filters for filtering of several (M) time multiplexed data streams in the same channel. However, the polyphase filters each have same number of filter coefficients as in a length of the original filter. Thus the amount of hardware is M times the hardware required for a direct implementation of a single filter. Moreover, the outputs of the filters are not combined as a polyphase channelizer. Hence, there is no FFT processor as is required for combining the polyphase filters outputs. Limberg does not teach polyphase channelization. These and other disadvantages are solved or reduced using the invention.